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On Taking the $D\to 4$ limit of Gauss-Bonnet Gravity: Theory and Solutions

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arxiv 2004.09472 v2 pith:QNGIMLVN submitted 2020-04-20 gr-qc hep-th

Robie A. Hennigar , David Kubiznak , Robert B. Mann , Christopher Pollack This is my paper · ORCID
classification gr-qchep-th
keywords gravitytheorygauss-bonnetlimitdimensionssolutionsdefinedfour
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abstract

We comment on the recently introduced Gauss-Bonnet gravity in four dimensions. We argue that it does not make sense to consider this theory to be defined by a set of $D\to 4$ solutions of the higher-dimensional Gauss-Bonnet gravity. We show that a well-defined $D\to 4$ limit of Gauss-Bonnet Gravity is obtained generalizing a method employed by Mann and Ross to obtain a limit of the Einstein gravity in $D=2$ dimensions. This is a scalar-tensor theory of the Horndeski type obtained by a dimensional reduction methods. By considering simple spacetimes beyond spherical symmetry (Taub-NUT spaces) we show that the naive limit of the higher-dimensional theory to four dimensions is not well defined and contrast the resultant metrics with the actual solutions of the new theory.

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Cited by 10 Pith papers

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